Question

Write the numbers whose multiplicative inverses are the numbers themselves

Answer 1

The numbers whose multiplicative inverses are the numbers themselves are - 1 and 1

Given :

The numbers whose multiplicative inverses are the numbers themselves

To find :

The numbers

Solution :

Step 1 of 2 :

Define multiplicative inverse of a number

1 is the Multiplicative identity

Let M is the multiplicative inverse of N ( ≠ 0 )

Then M × N = 1 = N × M

⇒ M = 1/N

So 1/N is multiplicative inverse of N

Step 2 of 2 :

Find the numbers

Let N be the required number

Then multiplicative inverse of N is N

By the given condition

$\displaystyle \sf{ N \times N = 1}$

$\displaystyle \sf{ \implies {N}^{2} = 1 }$

$\displaystyle \sf{ \implies N = \pm \: \sqrt{1} }$

$\displaystyle \sf{ \implies N = \pm \: 1 }$

Hence the numbers whose multiplicative inverses are the numbers themselves are - 1 and 1